The school Euclid: comprising the first four books, by A.K. Isbister |
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Αποτελέσματα 1 - 5 από τα 6.
Σελίδα 5
Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . IX . The whole is greater than its part . X. Two straight lines cannot inclose a space . XI .
Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . IX . The whole is greater than its part . X. Two straight lines cannot inclose a space . XI .
Σελίδα 9
therefore AC shall coincide with DF ; and because AC is equal to DF , wherefore also the point C shall coincide with the point F. But the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF ...
therefore AC shall coincide with DF ; and because AC is equal to DF , wherefore also the point C shall coincide with the point F. But the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF ...
Σελίδα 15
therefore the point C shall coincide with the point F ; wherefore BC coinciding with EF , BA and AC shall coincide with ED and DF ; for if the base BC coincides with the base EF , but the sides BA , CA do not coincide with the sides ED ...
therefore the point C shall coincide with the point F ; wherefore BC coinciding with EF , BA and AC shall coincide with ED and DF ; for if the base BC coincides with the base EF , but the sides BA , CA do not coincide with the sides ED ...
Σελίδα 108
Upon the same straight line , and upon the same side of it , there cannot be two similar segments of circles , not coinciding with one another . ( References - Prop . 1. 16 ; III . 108 [ BOOK III . THE SCHOOL EUCLID .
Upon the same straight line , and upon the same side of it , there cannot be two similar segments of circles , not coinciding with one another . ( References - Prop . 1. 16 ; III . 108 [ BOOK III . THE SCHOOL EUCLID .
Σελίδα 109
11 ) the angle ACB must be equal to the angle ADB , the exterior to the interior , which is impossible ; ( 1. 16 ) Therefore there cannot be two similar segments of circles upon the same side of the same line , which do not coincide .
11 ) the angle ACB must be equal to the angle ADB , the exterior to the interior , which is impossible ; ( 1. 16 ) Therefore there cannot be two similar segments of circles upon the same side of the same line , which do not coincide .
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The School Euclid: Comprising the First Four Books, by A.K. Isbister Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
The School Euclid: Comprising the First Four Books, by A.K. Isbister Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD angle ABC angle BAC angle BCD angle equal assumed base base BC BC is equal bisect centre circle ABC circumference coincide common constr CONSTRUCTION DEMONSTRATION describe diameter distance divided double draw Edition equal to AC equilateral and equiangular exterior angle extremity fall figure four given circle given straight line greater half impossible inscribed join less Let ABC likewise manner meet opposite angles parallel parallelogram pass pentagon perpendicular produced proved Q. E. D. PROP reason rectangle contained References-Prop remaining angle right angles segment semicircle shown side BC sides square of AC straight line AC THEOREM third touches the circle triangle ABC twice the rectangle wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 141 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Σελίδα 35 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Σελίδα 71 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle...
Σελίδα 33 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Σελίδα 61 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square of...
Σελίδα 43 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Σελίδα 27 - ... shall be greater than the base of the other. Let ABC, DEF be two triangles, which have the two sides AB, AC, equal to the two DE, DF, each to each, viz.
Σελίδα 77 - An angle in a segment is the angle contained by two straight lines drawn from any point in the circumference of the segment to the extremities of the straight line which is the base of the segment.
Σελίδα 15 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles.
Πληροφορίες βιβλιογραφίας
| Τίτλος | The school Euclid: comprising the first four books, by A.K. Isbister |
| Συγγραφέας | Euclides |
| Επιμελητής | Alexander Kennedy Isbister |
| Εκδόθηκε | 1862 |
| Πρωτότυπο από | Πανεπιστήμιο Οξφόρδης |
| Ψηφιοποιήθηκε στις | 18 Απρ. 2006 |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |